The data set is about the number of opioid overdose deaths and population in each county in Georgia in 2020. The goal of this study is to examine county-level measures of social vulnerability and access to health care in relation to observed overdose mortality rates. Specifically, we aim to identify county-level factors associated with opioid mortality in Georgia, focusing on measures of social vulnerability such as poverty, unemployment, housing vacancy, urbanization, and access to health care and treatment.
## Rows: 159
## Columns: 45
## $ NAME <chr> "Rabun", "Towns", "Fannin", "Murray", "Whitf…
## $ FIPS <chr> "13241", "13281", "13111", "13213", "13313",…
## $ county <chr> "241", "281", "111", "213", "313", "047", "2…
## $ rucc_code13 <fct> non, non, non, sm, sm, mm, non, mm, mm, non,…
## $ rucc_code13_n <dbl> 6, 6, 6, 4, 4, 3, 6, 3, 3, 6, 5, 6, 6, 5, 5,…
## $ mortality <dbl> 4, 3, 5, 6, 15, 10, 2, 13, 4, 6, 10, 8, 7, 7…
## $ population <dbl> 16602, 11506, 25322, 39782, 104658, 66550, 2…
## $ incidence <dbl> 2.409348e-04, 2.607335e-04, 1.974568e-04, 1.…
## $ mort_rate <fct> High, High, Moderate, Moderate, Moderate, Mo…
## $ Year <dbl> 2020, 2020, 2020, 2020, 2020, 2020, 2020, 20…
## $ state <chr> "13", "13", "13", "13", "13", "13", "13", "1…
## $ pct_poverty <dbl> 13.6, 8.9, 7.6, 11.8, 11.3, 7.2, 12.1, 10.4,…
## $ vacancy_rate <dbl> 44.6, 39.6, 36.1, 10.3, 9.5, 8.8, 31.1, 13.6…
## $ unemployment_rate <dbl> 4.1, 4.2, 5.8, 6.5, 6.0, 3.5, 4.8, 6.8, 5.0,…
## $ unemployment_rate_out <dbl> 4.1, 4.2, 5.8, 6.5, 6.0, 3.5, 4.8, 6.8, 5.0,…
## $ pct_black <dbl> 2.0, 1.8, 0.8, 1.3, 4.5, 3.7, 1.0, 5.2, 2.1,…
## $ dist_to_usroad <dbl> 177471.982, 228978.344, 177934.752, 65169.38…
## $ dist_to_treatment <dbl> 1566.7539, 384.2369, 3281.9039, 1459.7800, 7…
## $ dist_to_bupren <dbl> 1566.7539, 384.2369, 7290.4924, 1459.7800, 7…
## $ dist_to_hrsa <dbl> 3617.9437, 108638.0823, 3281.9039, 1873.8104…
## $ dist_to_mh <dbl> 117386.2983, 67711.6173, 109015.1163, 133829…
## $ dist_to_otp <dbl> 102674.625, 63619.676, 113680.107, 4003.911,…
## $ dist_to_su <dbl> 100824.502, 63619.676, 79736.498, 4005.876, …
## $ pct_poverty_std <dbl> -0.15651142, -0.98484701, -1.21396111, -0.47…
## $ vacancy_rate_std <dbl> 3.08075917, 2.51252486, 2.11476084, -0.81732…
## $ unemployment_rate_std <dbl> -0.74498218, -0.70715012, -0.10183723, 0.162…
## $ unemployment_rate_out_std <dbl> -0.793303461, -0.751995315, -0.091064977, 0.…
## $ pct_black_std <dbl> -1.5609990, -1.5723595, -1.6291621, -1.60076…
## $ dist_to_usroad_std <dbl> 0.937440982, 1.530272550, 0.942767405, -0.35…
## $ dist_to_treatment_std <dbl> -0.45673954, -0.52253888, -0.36130264, -0.46…
## $ dist_to_bupren_std <dbl> -0.87400434, -0.89896047, -0.75320913, -0.87…
## $ dist_to_hrsa_std <dbl> -0.5575937, 3.0368235, -0.5690950, -0.617288…
## $ dist_to_mh_std <dbl> 1.04483333, 0.11887284, 0.88879038, 1.351338…
## $ dist_to_otp_std <dbl> 0.35664472, -0.31610445, 0.54622196, -1.3430…
## $ dist_to_su_std <dbl> 0.68693705, 0.03854784, 0.31942467, -1.00037…
## $ RPL_THEME1 <dbl> 0.5380, 0.1519, 0.2911, 0.5253, 0.7405, 0.03…
## $ RPL_THEME2 <dbl> 0.5380, 0.0380, 0.3797, 0.2342, 0.7405, 0.20…
## $ RPL_THEME3 <dbl> 0.0696, 0.0063, 0.0000, 0.1456, 0.5570, 0.04…
## $ RPL_THEME4 <dbl> 0.1772, 0.2658, 0.1392, 0.5316, 0.7215, 0.22…
## $ RPL_THEMES <dbl> 0.3038, 0.1013, 0.1709, 0.4241, 0.7468, 0.07…
## $ rucc_code13_4 <fct> mi_non, mi_non, mi_non, mm_sm, mm_sm, mm_sm,…
## $ rucc_code13_5 <fct> Micropolitan & Non-Metro, Micropolitan & Non…
## $ Name <chr> "Clayton", "Hiawassee", "Blue Ridge", "Chats…
## $ Name_Seat <chr> "Clayton", "Hiawassee", "Blue Ridge", "Chats…
## $ geometry <MULTIPOLYGON [US_survey_foot]> MULTIPOLYGON (((88…
| Characteristic | Overall N = 1591 |
Mortality rate
|
p-value2 | ||
|---|---|---|---|---|---|
| Low N = 591 |
Moderate N = 611 |
High N = 391 |
|||
| Rural-Urban Continuum Code | 0.008 | ||||
| Â Â Â Â Large Central Metro & Large Fringe Metro | 29 (18%) | 5 (8.5%) | 18 (30%) | 6 (15%) | |
| Â Â Â Â Medium Metro | 15 (9.4%) | 3 (5.1%) | 10 (16%) | 2 (5.1%) | |
| Â Â Â Â Small Metro | 30 (19%) | 15 (25%) | 8 (13%) | 7 (18%) | |
| Â Â Â Â Micropolitan & Non-Metro | 85 (53%) | 36 (61%) | 25 (41%) | 24 (62%) | |
| Mortality Count | 3 (1, 8) | 1 (0, 2) | 5 (2, 14) | 6 (4, 9) | <0.001 |
| Population | 22,736 (11,319, 57,089) | 21,498 (10,343, 43,014) | 27,113 (17,277, 91,600) | 20,533 (12,830, 35,871) | 0.040 |
| Poverty rate | 14.0 (10.1, 18.1) | 16.6 (12.7, 20.0) | 11.7 (8.7, 16.6) | 13.8 (10.0, 17.0) | 0.002 |
| Vacancy rate | 16 (12, 21) | 16 (14, 22) | 14 (10, 19) | 19 (12, 27) | 0.042 |
| Unemployment rate | 5.70 (4.30, 7.10) | 5.80 (4.20, 8.60) | 5.60 (4.70, 6.50) | 5.40 (4.20, 6.60) | 0.5 |
| Percentage of Black Population | 29 (17, 41) | 31 (25, 47) | 25 (12, 36) | 30 (11, 41) | 0.012 |
| Distance to interstate | 82,400 (21,221, 136,715) | 91,434 (47,270, 151,954) | 63,322 (11,994, 105,432) | 95,883 (39,549, 147,643) | 0.026 |
| Distance to treatment | 3,191 (1,783, 5,730) | 3,627 (1,999, 5,476) | 3,120 (1,713, 5,404) | 2,820 (1,567, 5,949) | 0.4 |
| 1 n (%); Median (Q1, Q3) | |||||
| 2 Fisher’s exact test; Kruskal-Wallis rank sum test | |||||
U.S. Department of Health and Human Services, Substance Abuse and Mental Health Services Administration, Behavioral Health Services Information System. (2024). FindTreament_Facility_listing. Retrieved from https://findtreatment.gov/locator.
Quitman County has the longest distance to treatment centers at 185,132 feet, followed by Warren (164,830 feet), Stewart (161,331 feet), Glascock (160,496 feet), and Randolph (153,437 feet) counties.
Counties in southwestern and rural central Georgia generally have longer distances to treatment centers.
\[
y_i|\mu_i \sim \text{Poisson}(\mu_i), \\ where \ \mu_i = E(y_i) =
Var(y_i)
\\\
\\
\log\left(\frac{\mu_i}{pop_i}\right) = \beta_0 +
\beta_1\,poverty\_rate_i + \beta_2\,vacancy\_rate_i +
\beta_3\,unemployment\_rate_i + \beta_4\,pct\_black_i +
\beta_5\,dist\_to\_road_i + \beta_6\,dist\_to\_treatment_i + \theta_i
\\\
\\
\log(\mu_i) = \log(pop_i) + \beta_0 + \beta_1\,poverty\_rate_i +
\beta_2\,vacancy\_rate_i + \beta_3\,unemployment\_rate_i +
\beta_4\,pct\_black_i + \beta_5\,dist\_to\_road_i +
\beta_6\,dist\_to\_treatment_i + \theta_i
\\\
\\
\theta_i \sim N(0,\tau^2)
\]
\(y_i\) : mortality count for county i
\(\mu_i\) : expected mortality count for county i
\(\log pop_i\) : population of county i, used as an offset to adjust for the different population sizes across the counties
\(\beta_0\) : baseline log expected mortality rate
\(\theta_i\) : random intercept for county i, county-specific deviation in baseline log expected mortality rate
\(e^{\beta_1}\) : relative mortality rate change for a one standard deviation increase in the poverty rate
\(e^{\beta_2}\) : relative mortality rate change for a one standard deviation increase in the vacancy rate
\(e^{\beta_3}\) : relative mortality rate change for a one standard deviation increase in the unemployment rate
\(e^{\beta_4}\) : relative mortality rate change for a one standard deviation increase in the percentage of black population
\(e^{\beta_5}\) : relative mortality rate change for a one standard deviation increase in the distance to the interstate
\(e^{\beta_6}\) : relative mortality rate change for a one standard deviation increase in the distance to the treatment center
# Fit the poisson regression model
dat$log_pop = log(dat$population)
fit = glmer(mortality ~ offset(log_pop) + pct_poverty_std + vacancy_rate_std +
unemployment_rate_out_std + pct_black_std + dist_to_usroad_std +
dist_to_treatment_std + (1|county),
family = poisson(link = "log"), data = dat)
summary(fit)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula: mortality ~ offset(log_pop) + pct_poverty_std + vacancy_rate_std +
## unemployment_rate_out_std + pct_black_std + dist_to_usroad_std +
## dist_to_treatment_std + (1 | county)
## Data: dat
##
## AIC BIC logLik deviance df.resid
## 761.1 785.7 -372.6 745.1 151
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.36268 -0.55601 -0.04554 0.36658 2.82659
##
## Random effects:
## Groups Name Variance Std.Dev.
## county (Intercept) 0.1924 0.4386
## Number of obs: 159, groups: county, 159
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.94207 0.06144 -145.537 <2e-16 ***
## pct_poverty_std 0.01544 0.07800 0.198 0.8431
## vacancy_rate_std 0.17329 0.06984 2.481 0.0131 *
## unemployment_rate_out_std -0.13403 0.07617 -1.760 0.0785 .
## pct_black_std -0.07184 0.06537 -1.099 0.2718
## dist_to_usroad_std -0.17937 0.07751 -2.314 0.0207 *
## dist_to_treatment_std -0.03017 0.06534 -0.462 0.6443
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pct_p_ vcnc__ unm___ pct_b_ dst_t_s_
## pct_pvrty_s 0.121
## vcncy_rt_st 0.087 -0.351
## unmplymn___ 0.108 -0.193 0.099
## pct_blck_st -0.028 -0.397 0.061 -0.346
## dst_t_srd_s 0.189 -0.261 -0.336 0.001 0.185
## dst_t_trtm_ 0.129 0.034 -0.103 0.024 0.015 0.068
The baseline relative mortality rate is \(e^\hat{\beta_0}\) = \(e^{-8.93}\) = 0.0001.
There exists heterogeneity in baseline mortality
rate with a between-county standard deviation \(\tau\) of 0.44.
So
95% of the counties have baseline mortality rates between \(e^{-8.93 \pm 1.96 \times 0.44}\) =
(0.00006, 0.0003).
There is evidence that mortality rate increases
by approximately 17.4% (\(e^\hat{\beta_2}\) = \(e^{0.16}\) = 1.174) for a one standard
deviation increase in the vacancy
rate.
There is evidence that mortality rate decreases by approximately 16.5% (\(e^\hat{\beta_5}\) = \(e^{-0.180}\) = 0.835) for a one standard deviation increase in the distance to the interstate.